Radiotherapy system

ABSTRACT

A radiotherapy system comprising a support for a patient undergoing radiotherapy treatment, a gantry rotatable about an axis, a source of radiation mounted on the gantry and producing a beam of radiation directed towards a target region of the patient, a collimator coupled to said radiation source, the collimator comprising a plurality of movable, beam-limiting elements, to collectively define a shaped aperture through which the radiation beam passes, a portal imager mounted on the gantry opposite the radiation source for detecting the radiation after it has passed through the patient and generating corresponding images, and associated circuitry for controlling at least the gantry, the source, the collimator, and the portal imager, collating detected data comprising a plurality of images acquired including images at a plurality of angles of rotation of said gantry and images at a plurality of collimator shapes; generating a three-dimensional image of the target region based thereon.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is a continuation of and claims priority of U.S.patent application Ser. No. 12/821,672, filed Jun. 23, 2010, the contentof which is hereby incorporated by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates to radiotherapy, and particularly relatesto methods and apparatus for reconstructing three-dimensional imagesfrom portal images acquired during radiotherapy treatment.

BACKGROUND ART

It is known that exposure of human or animal tissue to ionisingradiation will damage the cells thus exposed. This finds application inthe treatment of pathological cells, for example. In order to treattumours deep within the body of the patient, the radiation must howeverpenetrate the healthy tissue in order to irradiate and destroy thepathological cells. In conventional radiation therapy, large volumes ofhealthy tissue can thus be exposed to harmful doses of radiation,potentially resulting in unacceptable side-effects. It is thereforedesirable to design a device for treating a patient with ionisingradiation and treatment protocols so as to expose the pathologicaltissue to a dose of radiation which will result in the death of thosecells, whilst keeping the exposure of healthy tissue to a minimum.

Several methods have previously been employed to achieve the desiredpathological cell-destroying exposure whilst keeping the exposure ofhealthy cells to a minimum. Many methods work by directing radiation ata tumour from a number of directions, either simultaneously frommultiple sources or multiple exposures over time from a single movablesource. The dose deposited from each direction is therefore less thanwould be required to destroy the tumour, but where the radiation beamsfrom the multiple directions converge, the total dose of radiation issufficient to be therapeutic. By providing radiation from multipledirections, the damage caused to surrounding healthy cells can bereduced.

Intensity modulated arc therapy (IMAT) is one method of achieving this,and is described in U.S. Pat. No. 5,818,902. In this process, theradiation source is rotated around the patient, and the radiation beamcollimated to take a desired shape depending on the angle of rotation ofthe source, usually with a multi-leaf collimator (MLC). The potentialadvantages of a particular form of IMAT, volumetric modulated arctherapy (VMAT), have recently given rise to a number of commercialimplementations and research studies. In these systems, the dose rate,rotation speed and MLC leaf positions may all vary during delivery. Ingeneral, plans comparable in quality and accuracy to static-gantryintensity-modulated radiotherapy (IMRT) can be obtained, normally withreduced delivery times.

To make sure the radiation beams are correctly directed, the treatmentcan be guided by imaging of the target region, before or even during thetreatment. For example, kilovoltage computational tomography (CT) can beused during treatment by providing a separate source of imagingradiation mounted on the rotatable gantry, placed at an angle relativeto the main radiation head. A detector is positioned diametricallyopposite the source of imaging radiation, and collects imaging data fora plurality of rotational angles of the gantry. This data can then bereconstructed to form three-dimensional images using known CTtechniques. See PCT application WO 2006/030181 for an example of thismethod. Kilovoltage radiation is preferred for imaging due to the highcontrast between different structures in the patient.

An alternative method of imaging is to use the megavoltage radiation andan electronic imaging device. In this scheme, a radiation detector isplaced on the rotatable gantry diametrically opposite the main treatmenthead, and is designed to detect the megavoltage radiation after it haspassed through (and been attenuated by) the patient. The imagesgenerated are therefore individual transmission images, from the beam'seye view (BEV). Megavoltage imaging can be used to verify the positionof the MLC leaves in relation to the target within the patient. Theaperture thus created by the MLC leaves is known as a portal and hencethis form of imaging is often called ‘Portal imaging’ and the detectoran ‘electronic portal imaging device’ or EPID. However, the high energyassociated with therapeutic radiation is not ideal for imaging purposesas the attenuation coefficients of the various tissue types within apatient are similar at this energy level, leading to poor imagecontrast. In addition, this method is inherently two-dimensional becausein conventional radiotherapy the megavoltage beams are directed at thepatient from typically two to nine angles, which may be insufficient toprovide three-dimensional imaging.

It has been shown that CT reconstruction from megavoltage images (i.e.MVCT) is possible (see Pouliot J “Megavoltage imaging, megavoltage conebeam CT and dose-guided radiation therapy” 2007 Frontiers of RadiationTherapy and Oncology vol. 40, pp 132-42). However, for suchreconstructions, the megavoltage images need to be obtained before orafter the delivery of a treatment beam, using beams which generallyencompass the anatomy that is desired to be imaged and are therefore notpart of the radiation treatment. As this method does not make use ofportal images acquired during treatment (i.e. those acquired with thevarying MLC aperture of therapy) it is associated with an increase inundesired radiation dose to the patient.

A paper by Ruchala et al (“Megavoltage CT imaging as a by-product ofmultileaf collimator leakage”, 2000 Physics in Medicine and Biology,vol. 45, pp N61-70) discloses a method of reconstructingthree-dimensional CT images in tomotherapy. This process utilizes theleakage radiation through the closed leaves of a binary multi-leafcollimator (MLC), along with slight inefficiencies in treatmentdelivery, to generate MVCT images during treatment. However, the processis applicable only to tomotherapy, in which the leaves of the MLC areeither open or closed, i.e. binary. The portal images for CTreconstruction are acquired only when all leaves of the MLC are in theirclosed positions, i.e. the leakage radiation used to create the imagesalso generally encompasses the entire anatomy that is desired to beimaged.

What is required is an apparatus and a method for providing images of atarget region in a patient during radiotherapy. Conventional kilovoltageCT scanning requires significant additional equipment (e.g. an extrasource of radiation and a detector), leading to increased complexity andcost. Two-dimensional portal imaging suffers from reduced contrastbetween different internal structures, and it is frequently necessary tosupplement it by larger and/or orthogonal images taken prior to or aftertreatment. Megavoltage CT and these other two approaches thereforeincrease the undesired dose applied to the patient. These techniquesalso potentially increase the time required to treat the patient as theyrepresent an additional task for the operator to perform.

SUMMARY OF THE INVENTION

The present invention provides a method and apparatus for generatingthree-dimensional CT images of a target region in a patient during arotational are radiotherapy treatment. A portal imager detects theattenuated therapeutic radiation beam, and this data can be used toreconstruct a three-dimensional CT image. This technique avoids anyadditional radiation dose applied to the patient as the images areacquired simultaneously with the treatment delivery, thereby avoidingadditional time for acquisition.

The application of a cone-beam formula to portal images acquired duringa VMAT delivery does surprisingly lead to a readily recognizable CTvolume. Further, local (lambda) tomography can be used to enhance thevisual quality of the images. Such VMAT-CT reconstructions could be auseful tool for treatment position verification.

In one aspect of the present invention, there is provided a radiotherapysystem, comprising a support for supporting a patient undergoingradiotherapy treatment, a gantry that is rotatable about an axis, asource of radiation mounted on the gantry and producing a beam ofradiation directed towards a target region of the patient, a collimatorcoupled to said radiation source for collimating said radiation beam,the collimator comprising a plurality of beam-limiting elements, eachmovable to collectively define a shaped aperture through which theradiation beam passes, a portal imager mounted on the gantry oppositethe radiation source for detecting the radiation after it has passedthrough the patient and generating corresponding images, and associatedcircuitry for controlling at least the gantry, the source, thecollimator, and the portal imager, collating detected data comprising aplurality of images acquired from the imager including images at aplurality of angles of rotation of said gantry and images at a pluralityof collimator shapes, and generating a three-dimensional image of thetarget region based thereon.

In an embodiment, the associated circuitry is configured to apply analgorithm to the detection data, reconstructing values of an attenuationcoefficient for a plurality of locations in the target region.

The algorithm may set the attenuation coefficient to a null value forlocations lying outside the radiation beam for more than a thresholdrange of angles of rotation of the gantry. In this way, the image is notdegraded by attempting to reconstruct values for the attenuationcoefficient for which there is insufficient data.

The algorithm may normalize the attenuation coefficient for eachlocation according to the range of angular rotation of the gantry inwhich that location was in the radiation beam, thus taking into accountthe fact that locations may not fall within the beam's eye view for thecomplete 2π arc of the radiation source. In order to achieve this, thealgorithm may comprise a masking function defining the positions of theMLC leaves.

The algorithm may extrapolate the detection data for locations fallingoutside of the radiation beam. One possible extrapolation scheme is toset a value for the detection data for locations extending beyond theedge of the radiation beam equal to the value for the detection data forthe location at the edge of the radiation beam.

In certain embodiments, the algorithm may comprise a smoothing anddeblurring function, which depends on detection data only for locationsfalling within a range of said location. Alternatively, the smoothingand deblurring function may be global, depending on all detection datafor a particular dimension.

BRIEF DESCRIPTION OF THE DRAWINGS

An embodiment of the present invention will now be described by way ofexample, with reference to the accompanying figures in which;

FIG. 1 is a schematic drawing of a radiotherapy system according toembodiments of the present invention;

FIG. 2 is a flowchart of a method according to embodiments of thepresent invention;

FIG. 3 a shows the geometry of the radiotherapy system according toembodiments of the present invention; and

FIG. 3 b shows the variables as seen from the beam's eye view.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1 shows a radiotherapy system 1 according to embodiments of thepresent invention.

Structurally, the system is similar to a conventional radiotherapyapparatus. The system comprises a gantry 10 on which is mounted a sourceof radiation 12 and, diametrically opposite the source 12, a radiationdetector 16. Such detectors are commonly referred to as portal imagers.The radiation source 12 is typically a linear accelerator producingx-rays or other penetrating radiation.

The gantry is rotatable about an axis 22. In the Figures, the gantry 10is depicted as a ring-shaped support. Alternatively, however, the gantrymay comprise a C-arm, with the source 12 and imager 16 on opposite arms.The isocentre of the system is defined as a plane running through therotation axis 22 of the gantry 10 perpendicular to the instantaneousaxis of the radiation beam.

A collimator 14 is coupled to the radiation source 12 in order tocollimate and shape the radiation beam. That is, a first collimation ofthe radiation (not illustrated) takes place close to the source 12. Thiscollimates the radiation produced by the source into a beam, e.g. acone- or fan-shaped beam diverging away from the source. A furthercollimator 14 then acts on this collimated beam in order to shape theradiation as required for therapy. An example of a suitable collimatorfor this aspect is a multi-leaf collimator (MLC). Such devices compriseone or more banks of parallel leaves, each of which can be moved in adirection transverse to the radiation beam axis. The leaves are moveableinto and out of the path of the radiation beam to a greater or lesserextent, and thus the combination of leaf positions collectively definesa shaped aperture through which radiation passes. In one embodiment, theMLC comprises two banks of leaves positioned on opposite sides of theradiation beam, with each leaf able to take any position with a rangefrom outside the radiation beam to crossing the radiation beam. In orderto sufficiently attenuate (i.e. block) the high-energy radiation, theleaves have a significant depth in a direction parallel to the radiationbeam axis, and are manufactured from high atomic number materials suchas tungsten. Thus, the output of the radiation source 12 and thecollimator 14 is a shaped radiation beam 24 directed generally inwardstowards the axis of rotation of the gantry.

Control and processing circuitry 26 is in communication with the gantry10, the source 12 and the collimator 14 and controls their operation.

A patient 20 is positioned on a support 18 for treatment such that atreatment target 21 (e.g. a tumour) is placed at the isocentre of thesystem. The longitudinal axis of the support and, thus, the patient 20usually but not necessarily lie substantially parallel to the rotationaxis 22 of the gantry. Various processes and apparatus for positioningand locating the patient will be familiar to those skilled in the art.In one embodiment, the support allows linear translation of the patientin three dimensions. The support 18 may also allow for tilting androtation of the patient 20, thus providing movement in up to six degreesof freedom (i.e. x, y, z, pitch, yaw and roll).

In operation, the system 1 performs the method as set out in FIG. 2. Themethod begins once the patient has been positioned correctly, i.e. withthe target at the isocentre.

Embodiments of the invention may also provide for motion of the patientduring treatment. For example, the support 18 may compensate formovement of the patient due to the respiratory or cardiac cycles (i.e.minimizing the motion of the target 21 relative to the system 1).Similarly, the movement and positioning of the collimator leaves maycompensate for such cyclical movement of the target 21. In theillustrated method, however, such processes are not considered forsimplicity.

In step 100, the method begins with the radiation source 12 generating aradiation beam. The radiation itself may be x-rays or other penetratingradiation as required.

In step 102, the radiation beam is collimated by action of thecollimator 14 to generate a shaped, collimated beam 24 for the purposesof therapy. For example, the beam may be shaped to conform to the shapeof the target, or a part of the target, or any other shape to achieve adesired dose distribution in and around the target. This beam isincident on the patient 20 and, inevitably, some of the radiation isabsorbed. The amount of absorption depends on the particular structureswithin the patient. In step 104, the attenuated radiation beam isdetected by the portal imager 16. The detection signals are converted todata and provided to the control circuitry 26. These data sets largelycomprise pixel data and can therefore (usually) be assembled intoviewable images. They will therefore be referred to as “images” in thisapplication, but this should not be interpreted to mean that the datasets must be stored in an image format, or that they must be viewed inan image form at any point. Often, the data sets will be transferred tothe processor for conversion into CT datasets without ever being viewedin an image form.

Steps 100, 102 and 104 generally all take place while the gantry 10rotates around the patient (step 106). Thus steps 100, 102, 104 and 106may all take place substantially simultaneously. That is, the gantry 10rotates around the patient, while the source 12 continuously generates aradiation beam and the collimator leaves move to new positions. Thecontrol circuitry 26 controls this operation, and may vary the radiationenergy, the dose rate, the collimator positions and the speed ofrotation of the gantry throughout the process.

The method then proceeds to step 108 in which the circuitry 26 appliesan algorithm to the portal image data and reconstructs athree-dimensional CT image of the target region. There is no fixed timeat which the algorithm is applied. The algorithm acts on the data thathas been acquired up until the point the algorithm is invoked. If athree-dimensional CT image is required during treatment, the algorithmmay be invoked during treatment. The CT image can then be used to guidethe therapy for the remainder of the treatment. Alternatively, the CTimage may be generated after treatment to assist the determination ofthe dosage distribution delivered to the patient, or to record theinternal motion of the patient's tissues. Generally, however, the moredata that is acquired, the better the quality of the CT image that isobtained.

The CT image so generated is a measure of the attenuation at any onepoint in three-dimensions within the target region. Thus, in oneembodiment, the attenuation coefficient itself ƒ(r,φ,z) is found (where(r,φ,z) are cylindrical polar coordinates). In alternative embodiments,the variable that is reconstructed may be an alternative quantity thatis nonetheless related to the attenuation coefficient and providesuseful imaging information. Hereinafter, the term “attenuationcoefficient” is taken to mean the attenuation coefficient ƒ(r,φ,z) aswell as these related quantities.

The algorithm that is applied in step 108 allows the generation of athree-dimensional image from portal images despite many challenges. Theportal images have a very narrow field of view of the target, as thecollimator leaves act to block any radiation that is not directedtowards the target in order to minimize the damage to surroundinghealthy tissue. Moreover, the positions of the collimator leaves maychange as the gantry rotates around the patient. Thus, the field of viewat one angle of rotation will not in general be the same as the field ofview in another angle of rotation.

The algorithm has several mathematical components, each of whichact—both alone and in combination—to overcome these difficulties.

A first part of the algorithm relates to an acknowledgement that it maynot be possible to reconstruct the attenuation coefficient for alllocations within the target region. First, it is impossible to imagelocations that fall outside the target region entirely—and hence thepath of the radiation beam at all gantry rotation angles. There simplyis no data to reconstruct values from. However, there may be otherlocations within the target region which only fall within the path ofthe radiation beam for a subset of the gantry rotation angles. For theselocations, there may nonetheless be insufficient data to reconstruct anaccurate value for the attenuation coefficient. Reconstructing values ofthe attenuation coefficient for these locations may reduce the overallquality of the image. Thus, for each location within the target region,the first part of the algorithm sets the attenuation coefficient to anull value if that location falls outside the radiation beam for morethan a threshold angular extent. For example, that threshold may be setat 270°. In that case, if a location lies inside the radiation beam foronly 75° of the 360° revolution of the gantry, the attenuationcoefficient for that location is set to null. The null value may be zeroor any other value which in practice is regarded by the system as null.

A second part of the algorithm normalizes the reconstructed value of theattenuation coefficient for a particular location according to theangular range that location was inside the radiation beam. Thus, if aparticular location lies within the radiation beam for a fraction of acomplete revolution, the reconstructed attenuation coefficient for thatlocation is divided by that fraction. For example, if the location lieswithin the radiation beam for 180° (i.e. half of the possible gantryangles), the value of the attenuation coefficient may be multiplied bytwo to account for this.

Both of these parts of the algorithm may employ a masking function todefine the position of the collimator leaves at any particular rotationangle. In a plane orthogonal to the radiation beam axis, the maskingfunction is equal to zero for locations that are blocked by thecollimator leaves and one for locations that are open for radiation totravel through. The two variables used to define the location in thatplane may be parallel and orthogonal respectively to the direction oftravel of the collimator leaves, or at any angle with respect to theleaves.

Part of the algorithm is a measure of the energy received at the portalimager 16. Previously we have described that it may not be possible toreconstruct values of the attenuation coefficient for locations that lieoutside, or partially outside, the radiation beam during rotation of thegantry. However, in order to reconstruct values for locations that lieinside the radiation beam, it may nonetheless be necessary to estimatevalues for the energy that would have been received by the portal imagerfor those locations that lie outside the radiation beam. That is, “wouldhave been received” had the collimator leaves, for example, not blockedthe radiation. The received energy values can be extrapolated toestimate the energy received at these locations outside the beam. Oneexample is to set the received energy outside the right edge of theradiation beam equal to the received energy at the right edge of theradiation beam; likewise, the received energy outside the left edge ofthe radiation beam can be set equal to the received energy at the leftedge of the radiation beam. Other extrapolation schemes are possible,however.

Finally, the reconstructed attenuation coefficient may be subject to asmoothing and de-blurring operation. The smoothing and de-blurringoperation can be global, taking account of detected radiation across thewhole field of view, or local, taking account only of detected radiationwithin a range of the location being considered. In the latter case, therequirement to extrapolate the received energy is reduced and thereforethe accuracy of the reconstructed attenuation coefficient may begreater.

All of these features are embodied in the equation (14) described below.However, embodiments of the present invention may implement only one ormore of the algorithm features described above in order to reconstructattenuation coefficients from the portal images.

The present invention thus provides a method and an apparatus forreconstructing three-dimensional CT images from portal images acquiredduring treatment. Such a possibility was previously thought impossibledue to the narrow and ever-changing field of view, and the incompleteangular coverage of the reconstruction points by the rotating radiationsource (i.e. because of insufficient data). However, embodiments of thepresent invention can be greatly simplified compared to the imagingtechniques commonly employed conventional radiotherapy systems, whichtypically require a separate kilovoltage source of radiation anddetector.

Appendix

There now follows a mathematical description of the algorithm employedin step 108. The ‘global’ algorithm is shown in equation (10); thegeneral algorithm, including the global and ‘local’ algorithms, is shownin equation (14). A hybrid version, designed to incorporate the benefitsof both global and local algorithms, is shown in equation (16).

There is denoted a 3D function describing the attenuation coefficient ofa subject by the function, ƒ(r,φ,z), where (r,φ,z) are cylindrical polarcoordinates. In practice, either the Ram-Lak kernel (see Ramachandran GN and Lakshminarayanan A V 1971 “Three dimensional reconstruction fromradiographs and electron micrographs: applications of convolutionsinstead of Fourier transforms” Proceedings of the National Academy ofSciences US vol 68, pp 2236-2240, the contents of which are incorporatedherein by reference) or an apodizing kernel are applied in CTreconstruction. This results in the reconstruction not of ƒ(r,φ,z)itself, but rather this function smoothed by a point-spread function(PSF). In the case of a Ram-Lak kernel this PSF arises only from thefinite pixel-width. In the case of an apodizing kernel, additionalsmoothing may be included to reduce image noise. Consider such areconstructed “image” in the (r,φ) plane. The smoothed 3D function,ƒ(r,φ, z), can be expressed as,ƒ_(R)(r,φ,z)=E _(R)(r)**ƒ(r,φ,z),  (1)where E_(R)(r) is a 2D PSF in the (r,φ) plane and ** represents a 2Dconvolution operation. Now consider the cone-beam geometry illustratedin FIGS. 3 a and 3 b. The variables SAD and SDD are the source-to-axisdistance and source-to-detector distance, respectively. The variable βis the angle of the source with respect to the positive y-axis. Thevariables U and V denote the position of a point in the imaging plane.The Feldkamp cone-beam reconstruction algorithm (see Feldkamp L A, DavisL C and Kress J W 1984 “Practical cone-beam algorithm” Journal of theOptical Society of America A vol 1, pp 612-19, the contents of which areincorporated herein by reference) can then be written as,

$\begin{matrix}{{{f_{R}\left( {r,\phi,z} \right)} = {\frac{1}{2}{\int_{0}^{2\pi}\ {{\mathbb{d}{\beta\left( \frac{SAD}{{SAD} - s} \right)}^{2}}{\int_{- u_{\max}}^{u_{\max}}\ {{\mathbb{d}u}\mspace{14mu}{D_{\beta}\left( {u,v} \right)}{e_{R}\left( {u^{\prime} - u} \right)}\left( \frac{SAD}{\sqrt{{SAD}^{2} + u^{2} + v^{2}}} \right)}}}}}},} & (2)\end{matrix}$where,

$\begin{matrix}{{u = {U\left( \frac{SAD}{SDD} \right)}},{v = {V\left( \frac{SAD}{SDD} \right)}},} & (3) \\{u^{\prime} = {t\frac{SAD}{{SAD} - s}}} & (4) \\{{t = {r\mspace{14mu}{\cos\left( {\phi - \beta} \right)}}},{s = {r\mspace{14mu}{\sin\left( {\phi - \beta} \right)}}}} & (5)\end{matrix}$and D_(β)(u,v) is the cone-beam ray-projection at the point on thedetector defined by (u,v) for the source rotation, β. The function,e_(R)(u), is related to the PSF and takes the form,

$\begin{matrix}{{e_{R}(u)} \approx {\frac{1}{2\pi}{{\Lambda ɛ}_{R}(u)}}} & (6)\end{matrix}$where one possible form for ε_(R)(u) is

$\begin{matrix}\begin{matrix}{{{ɛ_{R}(u)} = {\frac{1}{R\sqrt{\pi}}\frac{\Gamma\left( {\frac{5}{2} + \alpha} \right)}{\Gamma\left( {2 + \alpha} \right)}\left( {1 - \left( \frac{u}{R} \right)^{2}} \right)^{\alpha + 1}}},\left. {if}\mspace{14mu} \middle| u \middle| {\leqq R} \right.} \\{{= 0},{otherwise}}\end{matrix} & (7)\end{matrix}$where R defines a range and Λ is the Calderon operator. The Calderonoperator is pseudo-differential operator that performs a de-blurringoperation. Consider a Euclidean space

″ in which a point is defined by the vector, r. A function in thisspace, ε(u), may have a Fourier transform, E(ρ), and a Fourier transformpair,

$\begin{matrix}{{E\left( \underset{\_}{\rho} \right)} = {{F\left\{ {ɛ\left( \underset{\_}{u} \right)} \right\}} = {{\int_{R^{''}}{{\mathbb{e}}^{{- 2}\pi\; i{\underset{\_}{u} \cdot \underset{\_}{\rho}}}\;{ɛ\left( \underset{\_}{u} \right)}\mspace{14mu}{and}\mspace{14mu}{ɛ\left( \underset{\_}{u} \right)}}} = {{F^{- 1}\left\{ {E\left( \underset{\_}{\rho} \right)} \right\}} = {\int_{R^{''}}{{\mathbb{e}}^{{+ 2}\pi\; i{\underset{\_}{u} \cdot \underset{\_}{\rho}}}{{E\left( \underset{\_}{\rho} \right)}.}}}}}}} & (8)\end{matrix}$The Calderon operator, acting on a function ε(u), is then defined asΛε( u )=F ⁻¹{2π|ρ|F{ε( u )}},  (9)where Λ acts on the n-dimensional space. In expression (6) the Calderonoperator acts on the scalar variable u only (i.e. n=1). Note that itwould also be possible to define e_(R)(u) as a standard global CTconvolution kernel, such as the Ram-Lak or Hamming kernel. This would,however, preclude the extension to local (lambda) reconstructiondiscussed subsequently.

Returning to equation (2), it is noted that the factors appearing in theround-brackets of this expression are geometric weighting factors. It isassumed for simplicity that SAD>>u,v and ignore such factors: thissimplifies the resulting formulae. Equation (2), however, is inadequate,as it stands, in dealing with the data insufficiencies in the projectiondata. The following VMAT-CT formula is therefore proposed,

$\begin{matrix}{{{f_{R}\left( {r,\phi,z} \right)} \approx {\frac{1}{2}\frac{\Theta\left( {{\int_{0}^{2\pi}{{M_{\beta}\left( {u^{\prime},v} \right)}\ {\mathbb{d}\beta}}} - \beta^{\prime}} \right)}{\frac{1}{2\pi}{\int_{0}^{2\pi}{{M_{\beta}\left( {u^{\prime},v} \right)}\ {\mathbb{d}\beta}}}}{\int_{0}^{2\pi}{\left\lbrack {{M_{\beta}\left( {u^{\prime},v} \right)}{\int_{- v_{\max}}^{u_{\max}}\ {{\mathbb{d}{{uD}_{\beta}^{extrap}\left( {u,v} \right)}}{e_{R}\left( {u^{\prime} - u} \right)}}}} \right\rbrack\ {\mathbb{d}\beta}}}}},} & (10)\end{matrix}$where the extra constituents are defined in detail below. The MLCaperture is described by the masking function, M_(β)(u,v). If theaperture extent, at a particular v, and β, is defined by the interval,u₁(v,β)<u<u₂(v,β), then a possible form for the masking function is

$\begin{matrix}{{M_{\beta}\left( {u,v} \right)} = {\begin{matrix}{1,} & {{{if}\mspace{14mu}{u_{1}\left( {v,\beta} \right)}} < u < {u_{2}\left( {v,\beta} \right)}} \\{0,} & {otherwise}\end{matrix}.}} & (11)\end{matrix}$

The acquired ray-projections should be extrapolated for the purposes ofthe convolution integral in (10). One possible extrapolation scheme is:

$\begin{matrix}{{D_{\beta}^{extrap}\left( {u,v} \right)} = {\begin{matrix}{{D_{\beta}\left( {u,v} \right)},} & {{{if}\mspace{14mu}{u_{1}\left( {v,\beta} \right)}} \leqq u \leqq {u_{2}\left( {v,\beta} \right)}} \\{{D_{\beta}\left( {u_{1},v} \right)},} & {{{if}\mspace{14mu} u} < {u_{1}\left( {v,\beta} \right)}} \\{D_{\beta}\left( {u_{2},v} \right)} & {{{if}\mspace{14mu} u} > {u_{2}\left( {v,\beta} \right)}}\end{matrix}.}} & (12)\end{matrix}$More sophisticated extrapolation schemes are, of course, possible. Thismakes no assumption about specific MLC orientation. However, with somecollimator rotations (e.g. 90°) it would be possible for leaves to splitthe aperture into more than a single region in the u-direction. Suchcases (not considered here) would require a slightly more complexmasking function and extrapolation. The masking function is includedinside the back-projection integral to prevent the back-projection ofconvolved ray-projections outside of the BEV. However, to obtain imagingdata of the target region, it is not important if the data set is notstrictly complete over an angular range. That said, where the data iswoefully insufficient the image quality will suffer, and thus a cut-offradian coverage, β′, may be included. This parameter appears in theHeaviside step-function, Θ(K), of equation (10). The Heaviside functionforces the reconstructed value to zero at positions in the BEV for lessthan β′ radians. This allows the elimination of reconstruction pointsfor which so little data are available that they are likely to bemisleading. The denominator of the fraction in which the Heavisidefunction appears is present to normalise the contributions according tothe angular extent of data available. Thus, for example, a voxel in theBEV for 75% of the 2π arc (i.e.

$\left( {{\text{i.e.}\mspace{14mu}\frac{1}{2\;\pi}{\int_{0}^{2\;\pi}{{M_{\beta}\left( {u^{\prime},v} \right)}{\mathbb{d}\beta}}}} = 0.75} \right),$∫₀ ^(2π)M_(β)(u′,v)dβ=0.75), will be divided by a factor 0.75 toapproximately correct for the missing contributions.

Due to data-insufficiencies in the set of projections obtained in a VMATtreatment, exact and unique reconstruction of f_(R)(r,φ,z) may not bepossible. The data-insufficiency in the VMAT-CT problem, in particular,the width truncation of projections by the MLC, suggests the possibilityof using local tomography techniques (see Faridani A, Ritman E L andSmith K T 1992 “Local Tomography” SIAM Journal of Applied Mathematicsvol 52, pp 459-484, the contents of which are incorporated herein byreference). The idea of local (lambda) CT is not to reconstructƒ_(R)(r,φ,z) but rather a related object,Λ^(mƒ) _(R)(r,φ,z)  (13)where m is an integer denoting the number of repeat operations of theCalderon operator. It is noted that in (13), Λ acts on the n=2 space of(r,φ) (but not over z). The new object (13) has many of the sameproperties as the original attenuation coefficient function. Thegeneralised version of the VMAT-CT reconstruction formula is then,

$\begin{matrix}{{{\Lambda^{m}{f_{R}\left( {r,\phi,z} \right)}} \approx {\frac{1}{2}\frac{\Theta\left( {{\int_{0}^{2\pi}{{M_{\beta}\left( {u^{\prime},v} \right)}\ {\mathbb{d}\beta}}} - \beta^{\prime}} \right)}{\frac{1}{2\pi}{\int_{0}^{2\pi}{{M_{\beta}\left( {u^{\prime},v} \right)}\ {\mathbb{d}\beta}}}}{\int_{0}^{2\pi}{\left\lbrack {{M_{\beta}\left( {u^{\prime},v} \right)}\ {\mathbb{d}u}\mspace{14mu}{D_{\beta}^{extrap}\left( {u,v} \right)}{e_{R}^{(m)}\left( {u^{\prime} - u} \right)}} \right\rbrack{\mathbb{d}\beta}}}}},} & (14)\end{matrix}$where the generalized function e_(R) ^((m))(u) is

$\begin{matrix}{{e_{R}^{(m)}(u)} \approx {\frac{1}{2\pi}\Lambda^{m + 1}{{ɛ_{R}(u)}.}}} & (15)\end{matrix}$If m is even, such as the m=0 case, e_(R) ^((m))(u) has a non-compactsupport and is termed “global”. The convolved ray-projection, to beback-projected, then depends on every unconvolved ray-projection alongthe u integration direction, for fixed values of v. Therefore, if thepatient does not entirely fit within the field-of-view at any angle β,required data are absent. Despite this, in some cases, theray-projections through the patient outside the acquired set can beextrapolated reliably enough to provide an acceptable reconstruction. Itcan be shown, however, that if m≧−1 and odd then e_(R) ^((m))(u) canhave a compact support and be described as “local”. This means that aconvolved ray-projection, to be back-projected, depends only on theunconvolved ray-projections in its local vicinity (within a distance Rin fact). Thus the m=1 algorithm has less restrictive data requirementsthan the m=0 case. In some cases therefore we might expect localtomography (m=1) to provide more useful information than the global(m=0) algorithm.

To encapsulate the benefits of either approach (local or globaltomography) a hybrid semi-local construction is proposed,Σ_(σ)ƒ_(R)(r,φ,z)=ƒ_(R)(r,φ,z)+σRΛƒ _(R)(r,φ,z),  (16)where σ is a dimensionless parameter and R is again the range parameter.

It will of course be understood that many variations may be made to theabove-described embodiment without departing from the scope of thepresent invention.

Although the present invention has been described with reference topreferred embodiments, workers skilled in the art will recognize thatchanges may be made in form and detail without departing from the spiritand scope of the invention.

The invention claimed is:
 1. A radiotherapy system, comprising: asupport for supporting a patient undergoing radiotherapy treatment; agantry, rotatable about an axis; a source of radiation, mounted on thegantry, producing a beam of therapeutic radiation directed towards atarget region of the patient; a collimator, coupled to said radiationsource, for collimating said therapeutic radiation beam, the collimatorcomprising a plurality of beam-limiting elements, moveable tocollectively define a shaped aperture through which the radiation beampasses; a portal imager, mounted on the gantry opposite the radiationsource, for detecting the therapeutic radiation after it has passedthrough the patient and generating corresponding images; and associatedcircuitry, for controlling at least the gantry, the source, thecollimator, and the portal imager, collating detected data consisting ofa plurality of images acquired from the imager, the plurality includingimages at a plurality of angles of rotation of said gantry and images ata plurality of collimator shapes, and generating a three-dimensionalimage of the target region based thereon.
 2. The radiotherapy systemaccording to claim 1, wherein the associated circuitry is configured toapply an algorithm to said detected data, reconstructing values of anattenuation coefficient for a plurality of locations in the targetregion.
 3. The radiotherapy system according to claim 2, wherein thealgorithm comprises a masking function describing the positions of thebeam-limiting elements.
 4. The radiotherapy system according to claim 2,wherein the algorithm extrapolates said detection data for locationsfalling outside of the radiation beam.
 5. The radiotherapy systemaccording to claim 4, wherein the extrapolation sets a value for thedetection data for locations extending beyond the edge of the radiationbeam equal to the value for the detection data for the location at theedge of the radiation beam.
 6. The radiotherapy system according toclaim 2, wherein the algorithm sets the attenuation coefficient to anull value for locations lying outside the radiation beam for more thana threshold range of angles of rotation of the gantry.
 7. Theradiotherapy system according to claim 2, wherein the algorithmnormalizes the attenuation coefficient for each location according tothe range of angular rotation of the gantry in which that location wasin the radiation beam.
 8. The radiotherapy system according to claim 2,wherein the algorithm comprises a smoothing and de-blurring function. 9.The radiotherapy system according to claim 8, wherein, for eachlocation, the smoothing and de-blurring function depends on detectiondata only for locations falling within a range of said location.
 10. Theradiotherapy system according to claim 1, wherein said therapeuticradiation beam is continuously generated as said gantry rotates.
 11. Amethod of generating three-dimensional images of a target region withina patient, in a system comprising a rotatable gantry, a source ofradiation mounted on the gantry for producing a beam of therapeuticradiation, a multi leaf collimator for collimating the radiation beam,and a detector mounted on the gantry opposite the source, the methodcomprising the steps of: for a plurality of angles of rotation of thegantry, detecting an attenuated radiation beam after it has passedthrough the target region, the attenuated radiation beam beingcollimated into a first shape for a first angle of rotation, and asecond, different shape for a second angle of rotation; collatingdetection data corresponding to the detected attenuated therapeuticradiation beam alone for said plurality of angles of rotation of saidgantry; and generating a three-dimensional image of the target regionbased on the collated detection data.
 12. The method according to claim11, wherein said generating step comprises applying an algorithm to saiddetection data, reconstructing values of an attenuation coefficient fora plurality of locations in the target region.
 13. The method accordingto claim 12, wherein the algorithm comprises a masking functiondescribing the positions of beam-limiting elements in the MLC.
 14. Themethod according to claim 12, wherein the algorithm extrapolates saiddetection data for locations falling outside of the radiation beam. 15.The method according to claim 14, wherein the extrapolation sets a valuefor the detection data for locations extending beyond the edge of theradiation beam equal to the value for the detection data for thelocation at the edge of the radiation beam.
 16. The method according toclaim 12, wherein the algorithm sets the attenuation coefficient to anull value for locations lying outside the radiation beam for more thana threshold range of angles of rotation of the gantry.
 17. The methodaccording to claim 12, wherein the algorithm normalizes the attenuationcoefficient for each location according to the range of angular rotationof the gantry in which that location was in the radiation beam.
 18. Themethod according to claim 12, wherein the algorithm comprises asmoothing and de-blurring function.
 19. The method according to claim18, wherein, for each location, the smoothing and de-blurring functiondepends on detection data only for locations falling within a range ofsaid location.
 20. The method according to claim 11, further comprising:controlling further collimation of said radiation beam on the basis ofsaid three-dimensional image.